As this collection's editors say in their introduction, it is increasingly common to acknowledge the mid-20^th century debate between Quine and Carnap as the ‘single most significant episode in the brief history of metaontological inquiry’ (1), and though it was once widely accepted that (i) the two were in fundamental opposition and (ii) Quine won their argument, both issues have become far more nuanced in recent years. In eleven essays by various thoughtful contributors (most being involved in the recent spike of interest in metaontology), Ontology After Carnap offers a range of arguments about ontology, from those deeply inspired by Carnap, through those seeking to co-opt parts of his work, to those who disagree with him fundamentally. Anyone interested in the history of analytic philosophy, or in metaontology, will find much of use in this volume.

It would not be possible here to do justice to every contribution, so to summarise the volume I will introduce several interrelated Carnapian ideas – frameworks, internal/external questions, analyticity, explication, and tolerance – and explain some of the more notable ways in which they are put to work, with occasional critical commentary.

Let us begin with the notion of a framework. For Carnap a framework is something like a language, or fragment thereof: for a family of terms, a framework gives rules for their appropriate use, with the number-framework telling us, e.g., to say that the number of Fs is three just when there exist some distinct x, y, and z such that they, and only they, are F. Amie Thomasson's contribution uses this idea to articulate what she believes is a neglected Carnapian approach to ontology. She blames the unpopularity of this position primarily on three things: (i) fear of verificationism, (ii) the belief that Quine fatally undermined Carnap's view, and (iii) Putnam's association of Carnapianism with ontological anti-realism. However, she thinks that a Carnapian position needn't involve any problems associated with (i)–(iii). The simple and persuasive idea that Thomasson recapitulates here (see also her Ontology Made Easy, 2015) is that once a framework is in place, provided it tells us a term's application and co-application conditions, we can very easily determine whether that term's intended referent exists. To see some unresolved issue here is a confusion, illustrated by the absurdity of continuing to ask the ‘external question’ (more on external questions later) whether there are numbers: on Thomasson's account this means questioning a term's legitimacy while ignoring the rules that are constitutive of its meaning. This simple way of putting things avoids talk of verificationism, and it avoids what Thomasson regards as an unfortunate association with anti-realism since, rather than holding that, e.g., nominalism and Platonism just give equally good alternative ‘versions’ of reality, on Thomasson's view Platonism obviously wins. In the only sense that the term ‘number’ has, the statement ‘There are numbers’ is true. Thomasson helpfully distances this result from so-called ‘quantifier variance’ views, since rather than saying that we may define the quantifier so that it does or not range over numbers, Carnap's nominalist lacks the expressive power to say ‘There are no numbers’; the introduction of the term itself puts in place the conditions that require us to assert that there are numbers.

Simon Evnine's piece argues that things are not so straightforward. There is, he claims, ‘too much content’ (149) to the concepts at issue for so-called ‘ontological minimalists’ to capture. Mereology provides a case study: Thomasson will say the concept fusion guarantees that fusions exist (since if some things exist, their fusion does). However Evnine identifies another aspect to the concept, captured by the definition of the fusion of some things as that which has exactly those things as parts. This grounds a dilemma. Either we define fusions using just the existence condition, which is easily met by the simple state of affairs, but then we don't know whether these things stand in the right relations, or we define fusions using both conditions, but then we cannot regard them as obviously existing because we have acknowledged that both existence and a certain relation are required. As Evnine puts it, aside from the deep nature of fusions, ‘what could possibly determine whether fusions, as defined by [the mere existence condition], also have the things on which they depend for existence as parts?’ (151) Any solution the minimalist offers, Evnine claims, will give up the truly minimal nature of the entities. For instance, he claims that this approach cannot work unless reference takes a back seat, yet appeal to sortal application conditions requires talk of reference. While his critique moves beyond standard ‘bad company’ objections to easy ontology, I doubt that it is compelling for a Carnapian of Thomasson's type. We cannot fully explain what we mean by ‘fusion’ using conditions that don't invoke fusions themselves, but it isn't clear why Thomasson must do so. She wants to erode the justification for denying that e.g., fusions exist – and the fact that we need to use ‘fusion’ to express some of the features we regard fusions as having is, one might think, grist to Thomasson's mill.

Elsewhere on the topic of frameworks, Alan Sidelle argues that there is some unclarity in the relation between Carnap and contemporary deflationists. Carnap held that ontological disputes are empty across all frameworks, while many contemporary deflationists think that there is something special – in a bad way – about physical ontology. Sidelle struggles to locate a justification for saying that questions of the form ‘Are there really Fs?’ can't be meaningfully asked at all, since nothing rules out the possibility of a framework for answering such questions. Sidelle proposes that we understand Carnap as challenging his opponents to come up with a clarification of ‘Are there really Fs?’ which doesn't mean something pointless like ‘Are Fs part of the F-framework?’. This allows contemporary deflationists to disagree with Carnap in some instances but not across the board, so long as they think that there is a good interpretation of the question for, say, debates in philosophy of mind, but not for physical ontology.

More hostile engagement with Carnap's frameworks can be found in Kathrin Koslicki's contribution. Her essay can be seen as a criticism of Carnap's view of ontological debate as centred on frameworks’ existential assumptions – though her objection extends to Quine's approach, which lacks separate frameworks but nonetheless treats ontology as about existential questions. According to Koslicki many ontological debates are not captured by asking existence-questions, and she makes her case using ‘pure’ and ‘impure’ trope theory. These theories agree on what exists – tropes and particulars – but disagree about how these relate. Pure trope theory sees tropes as more fundamental than particulars, and vice versa for impure trope theory. This leads the pure trope theorist to say that ‘free-floating’ tropes are possible while the transference of tropes between particulars is not, and vice versa for the impure trope theorist. Since this characterises their disagreement in a way both sides would accept, and does so in terms of fundamentality not existence, Koslicki concludes that Carnap (not to mention Quine) misses much of ontology's important content. It is helpful to see a clear example of what is supposedly missed by the ‘existential approach’, but one might wonder why this pure/impure contrast shouldn't be represented existentially. Both theories employ the term ‘trope’, but they associate it with different properties. Suppose we banned the shared term and instead asked for descriptions of the entities under debate; we would get different descriptions from the two theorists, which we could treat as identifying two putative kinds, K ₁ and K ₂ . The debate could then be described as over whether K ₁ s exist or K ₂ s exist. It is hard to see how this way of viewing things could be ruled out as illegitimate since doing so across the board would force us to take too seriously statements like ‘It turned out that the Ghost of Spooky Gorge was just Bill the Janitor with a puppet and a theremin!’ It doesn't seem appropriate to say that Scooby and the gang agree with the superstitious locals that the Ghost of Spooky Gorge exists.

Frameworks are of course important for Carnap's famous distinction, which has already arisen briefly, between internal and external questions. Alongside the idea that concepts come with associated frameworks stands Carnap's notion that there are two ways to ask an existence-question: internal to a framework, or external to any framework. If one asks ‘Do numbers exist?’ in the internal sense, they ask whether numbers are part of the number-framework, and this is easily resolved: they are. If one asks it in the external sense, Carnap thinks two things could be going on. Actual metaphysicians seem to be asking ‘Are there numbers independent of any framework?’ and Carnap can make no sense of this question, since frameworks are required to give the terms their meaning. He proposes instead that the external question be treated as something like ‘Should we adopt the number-framework?’, and while this is independent of any particular framework, he does not see it as concerning matters of fact. Rather it is merely pragmatic.

Hofweber's contribution takes up this distinction but modifies it heavily. He thinks that on any reasonable understanding of how Carnap actually distinguishes internal and external questions the claim that there are two ways of asking existence questions is false. First, according to Carnap the straightforward external question is not in fact a question but nonsense. On this understanding, since the pragmatic external question is not another way of asking the question but a proposal for how to make sense of a failed project, there is just one question. Alternatively there are a huge range of uninteresting things one could mean by asking ‘Are there numbers?’ so on this understanding there are many, many questions. Hofweber thinks that Carnap saw an important distinction, but got the wrong idea about its nature and significance. The genuine distinction, Hofweber claims,Footnote ¹ is between two ways of interpreting quantificational claims. On the ‘domain conditions’ reading, one asks ‘Are there Fs?’ to enquire whether, among the things out there in the world, Fs can be found. On the other hand, on the ‘inferential role’ reading, one asks ‘Are there Fs?’ to enquire whether some term can be substituted into certain statements. An example of the latter kind is if someone, based on a vague memory, says ‘There is someone Jeremy Hunt idolises,’ where it might be correct to substitute in, say, Richard Branson, but it might equally be correct to substitute a fictional villain like Mr Burns. Either way the sentence comes out true, and we are nonplussed if someone protests ‘But there's no such person as Mr Burns!’ The result, Hofweber thinks, is not that metaphysics lacks content and that we should rely just on science. Instead we either find that a discourse uses inferential role quantification, so its terms need not be taken especially seriously, or it uses domain conditions quantification, and therefore has serious commitments. In the latter case the role of metaphysics is still uncertain, since it is at least plausible that the domains themselves teach us about those discourses’ commitments.

If one is to motivate Carnap's frameworks, and thereby vindicate the internal/external distinction, the division of statements into analytic and synthetic is required. The rules of a framework can be supposed to guarantee that certain statements are true, and since these rules are in some sense relative to the framework, Carnap thinks, they are not substantively true but stipulated as true. It is this part of the edifice Carnap constructed that Quine has often been taken to undermine, but many have come to question Quine's critique, the contributors to this volume included. Thomasson points out, for instance, that Quine's request for a criterion of analyticity seems too demanding and that in later work Quine backtracks to accept some role for analyticity. I think this is a misinterpretation – in fact Quine accepts early on that Carnap's relativised notion of analyticity is reasonably clear, but doesn't think it will do the epistemological work that analyticity has been hoped to achieve. His later discussions of analyticity accept a non-threatening form of analyticity that confers no special epistemological status.

Some interesting work is done by Stephen Biggs and Jessica Wilson to examine the viability of Carnap's view of analyticity. They examine the claim that analyticity can be used to explain modal truths, which was an important part of Carnap's empiricism. Modal truths look mysterious to the empiricist, but if it turns out that modal truths are analytic we have a good explanation for their truth and their apriority (since we need only know the right semantic rules to know that they're true). This account gets into real trouble thanks to Kripke, since he proposes a range of cases of necessary a posteriori truth. Biggs and Wilson observe that epistemic two-dimensionalism, the response to Kripke that comes from a place most amenable to Carnap, would still be unacceptable to him since it relies on consulting intuitions and considering what is conceivable. The former idea is unclear, and Carnap will not accept a conceivability-based account because he regards natural-kind terms as generally too indeterminate to give us definite answers. Instead Carnap thinks we need explication to clarify the notions under consideration, and Biggs and Wilson argue persuasively that the abductive approach required for this should be considered a priori despite common assumptions to the contrary. They propose abductive two-dimensionalism as the best way of bringing Kripkean examples within the remit of Carnap's approach, though they argue that this solution undermines Carnap's metaphysical anti-realism. External ontological questions, we saw earlier, are supposed to be either meaningless through a lack of agreed standards or merely pragmatic, but if abduction is a method of arriving at truths, we must either say that this is an agreed standard for adjudicating between theories, or that pragmatic judgements have a certain categorical force.

I mentioned above the notion of explication. Gregory Lavers, in the most explicitly historical of the essays, looks at Carnap's use of this idea of ‘making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development’Footnote ² and argues that ‘[j]ust as Carnap sought to allow empiricists to overcome their nominalistic scruples, he himself should have more fully overcome his instrumentalist scruples’ (217). He persuasively argues that Carnap's attitude toward abstract objects matured from an early, formalistic phase, through Logical Syntax of Language and into the attitude in ‘Empiricism, Semantics, and Ontology’, where he thought the terminology of abstract objects could be suitably explicated in a way that showed them to be non-threatening to empiricist scruples. At first Carnap thought that truth and reference couldn't be explicated, but once Tarski showed they could, he abandoned this formalistic attitude. However he failed to do so when it came to unobservables, regarding talk of, e.g., electrons as mere expediency, and Lavers contends that this was inconsistent with his other views.

Moving on, several contributors focus on the principle of tolerance as providing Carnap's perspective on metaphysical disputes. Famously, Carnap holds that:

This suggests that we are licensed to criticise any language as unclear, but not as metaphysically problematic. Eli Hirsch explores this idea, identifying three possible degrees of Carnapian tolerance, which all involve treating an issue as ‘merely a matter of choosing a language’ (105). The first degree of tolerance is familiar from his previous work (e.g. ‘Ontology and Alternative Languages’ in Chalmers, Manley and Wasserman's Metametaphysics). The second degree of tolerance would involve embracing alternative languages without being able to state clearly how they relate to one's original language, an interesting idea but unfortunately rather unclear. The third, unacceptable degree of Carnapian tolerance, Hirsch says, is verificationism. I am unsure how Hirsch sees the connection to tolerance, as the role of verificationism in the collection is often just as bogeyman, a fearful outcome of taking Carnap too seriously that is never quite in focus.

In a short but interesting paper, Richard Creath takes a different stance on tolerance. He considers an objection from Matti Eklund (who also contributes to this volume) that Carnap's tolerant attitude collapses, since it requires an all-encompassing metalanguage in which to evaluate all object languages, which creates an inclusive framework from whose perspective the others are needlessly restrictive. Creath responds that Carnap does not need an overarching metalanguage, and indeed would see this as a bad idea since it would inevitably lead to us smuggling in particular metaphysical assumptions under a mask of neutrality. Instead we just need to be able to provide, for any object language, some metalanguage giving its statements’ truth-conditions. So for Creath, Eklund's claims misunderstand the significance of the principle of tolerance: it is not employed to let us definitively say from one perspective that all choices of language are equally good, but rather to say that, regardless of what perspective we take, we should acknowledge that other choices of language are possible. ‘In the new regime we are free to lay down whatever sentences we like as analytic,’ writes Creath, although ‘we have to be prepared to pay whatever practical price that involves.’ (195) Here, Carnap's tolerance is less minimal than the kind proposed by Hirsch, where we may believe what we wish because it makes no difference. It is a more thoroughgoing kind that acknowledges the possibility of important differences between frameworks while disavowing any attempt to provide a decisive external critique. I would have liked to see more of this constructive Carnap, including some consideration of what this kind of pragmatic approach would look like (e.g. what might qualify as a framework) and whether it contrasts with other kinds of pragmatism. However many of the contributions provide important groundwork for such projects.

This important collection further clarifies some of the interesting, and controversial, aspects of Carnap's ontological views in particular and of ‘Carnapian’ approaches in general. It also brings disagreements about them into dialogue, although it would in my opinion have been better still had there been more dialogue between contributors (where this happens, as in Eklund's and Creath's contributions, is where the collection is most informative). There is much more to be said about what influence Carnap's ideas have had, or should have, in analytic metaphysics, but further research will find a substantial body of work to respond to and build on here.